Set Theory and Algebra MCQ - Algebra

16:  

Match the following

A. Groups                         I. Associativity

B. Semi groups              II. Identity

C. Monoids                     III. Commutative
 
D. Abelian Groups         IV Left inverse

Codes. A B C D

A.

IV   I    II   III

B.

III    I   IV   II

C.

II   III   I   IV

D.

I    II    III   IV

 
 

Option: A

Explanation :


17:  

Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?

A.

(Z, *) is a monoid

B.

(Z, *) is an abelian group

C.

(Z, *) is a group

D.

None of these

 
 

Option: D

Explanation :


18:  

 Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?

A.

g = g-1 for every g ∈ G

B.

g = g2 for every g ∈ G

C.

(g o h) 2 = g2o h2 for every g,h ∈ G

D.

G is of finite order

 
 

Option: C

Explanation :


19:  

If the binary operation * is deined on a set of ordered pairs of real numbers as

(a, b) * (c, d) = (ad + bc, bd)

and is associative, then

(1, 2) * (3, 5) * (3, 4) equals

A.

(74,40)

B.

(32,40)

C.

(23,11)

D.

(7,11)

 
 

Option: A

Explanation :


20:  

If A = (1, 2, 3, 4). Let  ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is

A.

not anti-symmetric

B.

transitive

C.

reflexive

D.

symmetric

 
 

Option: B

Explanation :



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